Question:-In how many ways can a cricketer can score 240 runs with fours and sixes only?Choices:- 21 22 23 24

This problem can be solved using the concept of linear equations in two variables.

Let's denote the number of fours as x and the number of sixes as y.

Since each four gives 4 runs and each six gives 6 runs, and the total number of runs is 240, we can write the equation as:

4x + 6y = 240

We can simplify this equation by dividing all terms by 2:

2x + 3y = 120

Now, we need to find the number of integer solutions (x, y) for this equation, where both x and y are non-negative integers.

We can start by finding one solution. If x = 0, then y = 40. So, (0, 40) is one solution.

Now, we can find other solutions by decreasing y by 2 and increasing x by 3. This is because when we decrease y by 2, we need to increase x by 3 to keep the total the same.

So, the solutions are (0, 40), (3, 38), (6, 36), ..., (60, 0).

We can see that the number of solutions is the number of steps from 0 to 60 by 3, which is 60/3 + 1 = 21.

So, the cricketer can score 240 runs in 21 different ways using only fours and sixes.

Therefore, the correct answer is 21.